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Compact and noncompact structures in a class of nonlinearly dispersive equations. (English) Zbl 1013.35072
Summary: We study compact and noncompact dispersive structures formed by a class of nonlinear dispersive equations. We show that the focusing branches provide compactons solutions: solitons with compact support. We also show that the defocusing branches generate solitary patterns solutions. We test our work for a variety of nonlinear equations with positive and negative exponents.

35Q53KdV-like (Korteweg-de Vries) equations
37K40Soliton theory, asymptotic behavior of solutions
Full Text: DOI
[1] Rosenau, P.; Hyman, M. J.: Compactons: solitons with finite wavelengths. Phys. rev. Lett. 70, No. 5, 564-567 (1993) · Zbl 0952.35502
[2] Rosenau, P.: Nonlinear dispersion and compact structures. Phys. rev. Lett. 73, No. 13, 1737-1741 (1994) · Zbl 0953.35501
[3] Rosenau, P.: On nonanalytic solitary waves formed by a nonlinear dispersion. Phys. lett. A 230, No. 5/6, 305-318 (1997) · Zbl 1052.35511
[4] Rosenau, P.: On a class of nonlinear dispersive--dissipative interactions. Physica D 230, No. 5/6, 535-546 (1998) · Zbl 0938.35172
[5] Rosenau, P.: Compact and noncompact dispersive structures. Phys. lett. A 275, No. 3, 193-203 (2000) · Zbl 1115.35365
[6] P.J. Olver, P. Rosenau, Tri-Hamiltonian duality between solitons and solitary-wave solutions having compact support, Phys. Rev. E 53 (2) (1996) 1900--1906.
[7] Cooper, F.; Hyman, J.; Khare, A.: Compacton solutions in a class of generalized fifth-order Korteweg-de Vries equations. Phys. rev. E 64, No. 2, 1-5 (2001)
[8] Kivshar, Y.: Compactons in discrete lattices, nonlinear coherent struct. Phys. biol. 329, 255-258 (1994)
[9] Dinda, P. T.; Remoissenet, M.: Breather compactons in nonlinear Klein--Gordon systems. Phys. rev. E 60, No. 3, 6218-6221 (1999)
[10] Dusuel, S.; Michaux, P.; Remoissenet, M.: From kinks to compactonlike kinks. Phys. rev. E 57, No. 2, 2320-2326 (1998)
[11] Ludu, A.; Draayer, J. P.: Patterns on liquid surfaces: cnoidal waves, compactons and scaling. Physica D 123, 82-91 (1998) · Zbl 0952.76008
[12] Ismail, M. S.; Taha, T.: A numerical study of compactons. Math. comput. Simul. 47, 519-530 (1998) · Zbl 0932.65096
[13] Wazwaz, A. M.: New solitary-wave special solutions with compact support for the nonlinear dispersive $K(m,n)$ equations. Solitons and fractals 13, No. 22, 321-330 (2002) · Zbl 1028.35131
[14] Wazwaz, A. M.: Exact specific solutions with solitary patterns for the nonlinear dispersive $K(m,n)$ equations. Solitons and fractals 13, No. 1, 161-170 (2001)
[15] Wazwaz, A. M.: General compactons solutions for the focusing branch of the nonlinear dispersive $K(n,n)$ equations in higher dimensional spaces. Solitons and fractals 13, No. 20, 321-330 (2002) · Zbl 1028.35131
[16] Wazwaz, A. M.: A study of nonlinear dispersive equations with solitary-wave solutions having compact support. Math. comput. Simul. 56, 269-276 (2001) · Zbl 0999.65109
[17] A.M.Wazwaz, Solutions of compact and noncompact structures for nonlinear Klein--Gordon-type equation, Appl. Math. Comput. 134 (2/3) (2003) 487--500. · Zbl 1027.35119
[18] A.M.Wazwaz, Compactons and solitary patterns structures for variants of the KdV and the KP equations, Appl. Math. Comput. (2002), submitted for publication. · Zbl 0997.35083
[19] A.M. Wazwaz, The effect of the order of nonlinear dispersive equation on the compact and noncompact solutions, Appl. Math. Comput. (2002) submitted for publication.
[20] A.M. Wazwaz, A construction of compact and noncompact solutions for nonlinear dispersive equations of even order, Appl. Math. Comput. (2002), submitted for publication.
[21] Chertock, A.; Levy, D.: Particle methods for dispersive equations. J. comput. Phys. 171, 708-730 (2001) · Zbl 0991.65008
[22] Wazwaz, A. M.: A computational approach to soliton solutions of the Kadomtsev--petviashili equation. Appl. math. Comput. 123, No. 2, 205-217 (2001) · Zbl 1024.65098
[23] Wazwaz, A. M.: Construction of soliton solutions and periodic solutions of the Boussinesq equation by the modified decomposition method. Solitons and fractals 12, No. 8, 1549-1556 (2001) · Zbl 1022.35051
[24] A.M. Wazwaz, A First Course in Integral Equations, World Scientific, Singapore, 1997. · Zbl 0924.45001
[25] G. Adomian, Solving Frontier Problems of Physics: The Decomposition Method, Kluwer, Boston, 1994. · Zbl 0802.65122
[26] Adomian, G.: A review of the decomposition method in applied mathematics. J. math. Anal. appl. 135, 501-544 (1998) · Zbl 0671.34053